PEOGEESS OF MAGNETIC THEORY. 229 



aianner as to determine both their periodical variations (the changes 

 which occur in the period of a day, and of a year), the scculor 

 changes, as the gradual increase or diminution of the declination at 

 the same place for many years ; and the irregular fluctuations which, 

 as we have said, are simultaneous over a large part, or the whole, of 

 the earth's surface. 



AYhen these Facts have been ascertained over the whole extent of 

 the earth's surface, we shall still have to inquire what is the Cause of 

 the changes in the forces which these phenomena disclose. But as a 

 basis for all speculation on that subject, we must know the law of the 

 phenomena, and of the forces which immediately produce them. I 

 have already said that Euler tried to account for the Halleian ."ines 

 by means of two magnetic " poles," but that M. Hansteen conceived it 

 necessary to assume four. But an entirely new T light has been thrown 

 upon this subject by the beautiful investigations of Gauss, in his 

 Theory of Terrestrial Magnetism, published in 1839. He remarks 

 that the term " poles," as used by his predecessors, involves an as- 

 sumption arbitrary, and, as it is now found, false ; namely, that cer- 

 tain definite points, two, four, or more, acting according to the laws 

 of ordinary magnetical poles, will explain the phenomena. He starts 

 from a more comprehensive assumption, that magnetism is distributed 

 throuo-hout the mass of the earth in an unknown manner. On this 



O 



assumption he obtains a function V, by the differentials of which the 

 elements of the magnetic force at any point will be expressed. This 

 function V is well known in physical astronomy, and is obtained 

 by summing all the elements of magnetic force in each particle, each 

 multiplied by the reciprocal of its distance ; or as we may express 

 it, by taking the sum of each element and its proximity jointly. 

 Hence it has been proposed 16 to term this function the "integral 

 proximity" of the attracting mass." By using the most refined ma- 



10 Quart. Rev. JS'o. 131, p. 283. 



17 The function V is of constant occurrence in investigations respecting 

 attractions. It is introduced by Laplace in his investigations respecting tin- 

 attractions of spheroids, Mic. Cel. Livr. m. Art. 4. Mr. Green and Professor 

 Mac Cullagh have proposed to tei-m this function the Potential of the system ; 

 but this term (though suggested, I suppose, by analogy -with the substantive 

 Exponential], does not appear convenient in its form. On the other hand, the 

 term Integral Proximity does not indicate that which gives the function its 

 peculiar claim to distinction ; namely, that its differentials express the power 

 or attraction of the system. Perhaps Integral Potentiality, or Integral Attrac- 

 livity, would be a term combining the recommendations of both the others. 



